From my experience it is one of those things that you just have to get used to. The agilitys just don't like the cold, or the rain, especially the cold and rain together.
I does seems a little unusal that you would need to warm up that long if temps are still in the 60s, but as Word would say each scoot has their own personality. I find that even in the 50-60 degree range there is some warm-up involved, but usually reasonably gentle driving helps warm it up - alhtough there will be some hesitation for the first few minutes.
Taking 5 minutes to warm it up before you even try to ride if the scoot has been sitting outside in temps below 50 degrees isn't unusal in my experience. Depending how much cold weather you ride in, you might be up to 10 minutes of warm-up for temps below 30 degrees.